Lenz's Law Practice
A wire loop in the - plane sits in an external uniform magnetic field oriented at 30 degrees from the positive direction in the - plane, which increases in strength over time. In which direction does the induced magnetic field at the center of the wire loop point in the - plane?
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1 solution
The external magnetic field is increasing in time and the induced magnetic field will want to oppose its flux. The induced magnetic field must point either directly in the positive or negative z-direction at the center of the wire loop by symmetry: this magnetic field is due to the current in the loop. The magnitude of the current in the loop cares about the angle of the external magnetic field, but the direction of the current does not (outside of the overall sign).
Since the external field increases, the flux in the positive-z direction is increasing. So the induced magnetic field will point in the negative-z direction by Lenz's law to oppose this increase.